Finite Group Databasebeta

← #29568009

Subgroups — #29568009

Order 15616.

668 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#391×D61C211yesmaximal, characteristic
2#21445798C211yesmaximal, characteristic
3#21445576C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443644C211yesmaximal, characteristic, complemented
7C61×#1272C211yesmaximal, characteristic, complemented
8C22×Q8×D61C411yescharacteristic
9C2×C4⋊C4×D61C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519706—21no—
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×C8×Dic61—21no—
15#16839669C411yescharacteristic
16#16839668C2211yescharacteristic
17#16839667C411yescharacteristic
18#16839666—21no—
19#16839666—21no—
20#95×D61—21no—
21#95×D61—21no—
22#16839517C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122C2×C411yescharacteristic
29C2×Q8×D61—22no—
30C2×Q8×D61—42no—
31C2×Q8×D61—42no—
32C2×Q8×D61C814yescomplemented
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35C22×C4×D61C2×C411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×#92418—21no—
39C22×#92418—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C4⋊C4×D61—42no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C42×D61—42no—
47#14519706—42no—
48#14519689—24no—
49#14519689—42no—
50C8×Dic61—42no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63#95×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61C2×C812yes—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79Q8×D61—48no—
80Q8×D61—48no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—24no—
84C2×C4×D61—22no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61C2×C812yes—
96C2×C4×D61M1612yes—
97C2×C4×D61SD1612yes—
98C2×C4×D61Q1612yes—
99C2×Dic122—21no—
100C2×Dic122—24no—
101C2×Dic122—42no—
102C2×Dic122—42no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122C2×C812yes—
106C2×C8×C61—22no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—41no—
113C42×C61—41no—
114C4⋊Dic61—41no—
115#11758196—42no—
116C4×Dic61—22no—
117C4×Dic61—22no—
118C4×Dic61—41no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C23×C61C2×C22⋊C411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61C22⋊C812yes—
131C22×D61#10312yes—
132C22×D61#10412yes—
133Q8×C61—42no—
134Q8×C61—42no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C22×C811yescharacteristic
148C2×C4×C61C2×M1611yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61C2×Q1611yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—22no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61C22⋊C812yes—
165C2×Dic61#9912yes—
166C2×Dic61#10012yes—
167C2×Dic61#10312yes—
168C4×D61—24no—
169C4×D61—24no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—48no—
175C4×D61—84no—
176Dic122—42no—
177Dic122—48no—
178Dic122—42no—
179C8×C61—42no—
180C8×C61—81no—
181#92418—42no—
182#92418—81no—
183#7575—611nomaximal, Sylow
184C22×C61C2×C22⋊C811yescharacteristic
185C22×C61C2×#9911yescharacteristic
186C22×C61C2×#10011yescharacteristic
187C22×C61C2×#10311yescharacteristic
188C22×C61#41911yescharacteristic
189C22×C61C2×#10411yescharacteristic
190C22×C61#42111yescharacteristic
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—22no—
196C2×D61—22no—
197C2×D61Q8⋊C814yes—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—42no—
205C4×C61—81no—
206Dic61—22no—
207Dic61—42no—
208Dic61—41no—
209Dic61—81no—
210Dic61#32314yes—
211C2×#391—611no—
212#1797—611no—
213C4×C22⋊C8—611no—
214#1272—611no—
215#1272—611no—
216#1272—611no—
217#1272D6111yescharacteristic, complemented
218C2×C61C2×#32311yescharacteristic
219C2×C61C2×Q8⋊C811yescharacteristic
220C2×C61#147911yescharacteristic
221C2×C61#150811yescharacteristic
222C2×C61#152011yescharacteristic
223C2×C61#152711yescharacteristic
224C2×C61#154811yescharacteristic
225D61—24no—
226C23×Q8—611no—
227C22×C4⋊C4—611no—
228C22×C42—611no—
229C2×C4⋊C8—1221no—
230C2×C22⋊C8—1221no—
231C2×C22⋊C8—1221no—
232C2×C4×C8—1221no—
233#391—611no—
234#391—611no—
235#391—611no—
236#391—1221no—
237#391—1221no—
238#391C2×D6111yescharacteristic
239C2×#95—1221no—
240C2×#95—1221no—
241#336—611no—
242#336—611no—
243#336C2×D6111yescharacteristic
244#336C2×D6111yescharacteristic
245C61#757511yescharacteristic, complemented, Sylow
246C22×Q8—614no—
247C22×Q8—611no—
248C22×Q8—1221no—
249C22×Q8—1222no—
250C22×Q8—2442no—
251C22×Q8—2442no—
252C22×Q8C4×D6111yescharacteristic
253C23×C4—611no—
254C23×C4—611no—
255C23×C4—611no—
256C23×C4—1221no—
257C23×C4—1221no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—1221no—
261C22×C8—1221no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—2442no—
265C2×C4⋊C4C4×D6111yescharacteristic
266C2×C42—611no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—2442no—
270C2×C42C22×D6111yescharacteristic
271C4⋊C8—2442no—
272C22⋊C8—1224no—
273C22⋊C8—2442no—
274C4×C8—2442no—
275#95—21no—
276#95—21no—
277#95—1221no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95—1221no—
283C24—611no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—612no—
288C2×Q8—1224no—
289C2×Q8—1221no—
290C2×Q8—2441no—
291C2×Q8—2441no—
292C2×Q8—2442no—
293C2×Q8—2442no—
294C2×Q8—2448no—
295C2×Q8—2448no—
296C2×Q8C8×D6112yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1222no—
309C22×C4—1224no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2442no—
318C22×C4—2442no—
319C22×C4—2442no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4C2×C4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—1222no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C4⋊C4—41no—
338C4⋊C4—2441no—
339C4⋊C4—2442no—
340C42—41no—
341C42—1222no—
342C42—1222no—
343C42—2441no—
344C23—612no—
345C23—612no—
346C23—612no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23C22⋊C4×D6111yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—2442no—
355Q8—2442no—
356Q8—2448no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—612no—
372C2×C4—612no—
373C2×C4—1224no—
374C2×C4—1224no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1222no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4884no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2448no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4C2×C8×D6111yescharacteristic
393C2×C4M16×D6111yescharacteristic
394C2×C4SD16×D6111yescharacteristic
395C2×C4Q16×D6111yescharacteristic
396C2×C4#1451980611yescharacteristic
397C2×C4#1451980911yescharacteristic
398C8—42no—
399C8—81no—
400C8—4881no—
401C8—2442no—
402C22—614no—
403C22—1222no—
404C22—1222no—
405C22—1222no—
406C22—1222no—
407C22—1222no—
408C22—1222no—
409C22C22⋊C8×D6111yescharacteristic
410C22#99×D6111yescharacteristic
411C22#100×D6111yescharacteristic
412C22#103×D6111yescharacteristic
413C22#1683976911yescharacteristic
414C22#104×D6111yescharacteristic
415C22#1683977711yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—614no—
425C4—1222no—
426C4—4881no—
427C4—2442no—
428C4—2441no—
429C2—1224no—
430C2#323×D6111yescharacteristic
431C2Q8⋊C8×D6111yescharacteristic
432C2#2144421211yescharacteristic
433C2#2144433711yescharacteristic
434C2#2144438911yescharacteristic
435C2#2144441511yescharacteristic
436C2#2144449811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7575
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #21443645C2semidirect
5. #21443644C2semidirect
6. #21443644C2semidirect
7. C61×#1272C2semidirect
32. C2×Q8×D61C8semidirect
217. #1272D61semidirect
245. C61#7575semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#391×D612
#214457982
#214455762
#214436452
#214436442
C61×#12722
#757561